From Brett Hunter:

1) DIFC, DIFA, ZERO are never refined during a normal course 
  of refinement - only when calibrating (no lattice parameter 
  refinement in that case).  They correlate too strongly (1-to-1) to the 
  lattice parameters, and should, for TOF, be true instrument 
  parameters.

2) the alpha's and beta's should also be instrumental, unless 
   you believe that you have asymmetry, such as a compositional 
   variation in your sample.  
   Usually only alpha-1, beta-0 and beta-1 are non-zero in 
   any case. For HRPD-ISIS the alpha's are larger than say SEPD-IPNS
   due to the sharp rise and high resolution.  You may in the case
   of the alpha-1 get a large variation (with little or no improvement
   in fit) for HRPD-ISIS. As it doesn't affect anyhting - don't worry.

3) you may near the end of a refinement turn them on alpha/beta's to see 
   what happens - sometime a small improvement in fit is obtained.
   Unless you believe there is a physical reason for it, don't change 
   them from the instrumental values.

4) if you are far from the ideal peakshape/fit, a suggestion is to keep 
   sig-1 fixed at a readonable value, say 10-15.  Fix up as many of the
   other problems (such as lattice parameters etc), then refine sig-1.
   After that try gam-1.  Sometimes it is also best to put it further
   off a zero value, say at a value of 10, and then refine, that to refine
   directly from 0.0.  After that you can try sig-2 and gam-2.  

5) If your instrumental fit has no sig-0 and gam-0 components (eg HRPD-ISIS),
   then don't bother refining them until the end, if at all.